Let \(U\)  be an open subset such that \(V:= f^{-1}(U) \rightarrow U\)  is an isomorphism.
Note that \({{F}}\vert _U \subset T_U \cong T_V\) .
By [1]}, we have a coherent subsheaf \({{G}}\)  of \(T_Y\)  such that \({{G}}\vert _V = {{F}}\vert _U \subset T_V \) .
Then the pullback foliation \(f^*{{F}}\)  is defined to be the saturation of \({{G}}\) .
By [2]}, this definition is well-defined.
